How do you delete specific objects without deleting everything?
In Object mode you can create several objects, and to delete one or several of them, just select and press X.

If you select one object and enter in Edit mode, you can create several distinct meshes within this object, "distinct" meaning not linked between them by any edges.

Example: in Object mode, create a cube. Then select it, enter in Edit mode, and press shift A to create another cube within the object. The object now consists on 2 cubes.

As explained by Ashutosh, as long as these meshes are distinct you can select one or several of them, hovering your mouse over their vertices, edges or faces and pressing L. Or click one of its vertices, edges or faces and clicking ctrl L.

Now you can delete what you've selected or make it a separate object pressing P (Separate) > Selection. If you select all the meshes of an object and press P (Separate) > By Loose Parts it will create as many objects as you have distinct meshes.